Limits of sympathetic cooling of fermions: The role of the heat capacity of the coolant

The sympathetic cooling of an initially degenerate Fermi gas by either an ideal Bose gas below $T_c$ or an ideal Boltzmann gas is investigated. It is shown that the efficiency of cooling by a Bose gas below $T_c$ is by no means reduced when its heat capacity becomes much less than that of the Fermi gas, where efficiency is measured by the decrease in the temperature of the Fermi gas per number of particles evaporated from the coolant. This contradicts the intuitive idea that an efficient coolant must have a large heat capacity. In contrast, for a Boltzmann gas a minimal value of the ratio of the heat capacities is indeed necessary to achieve T=0 and all of the particles must be evaporated.Comment: 5 pages, 3 figure

Bose-Einstein condensation in an optical lattice

In this paper we develop an analytic expression for the critical temperature for a gas of ideal bosons in a combined harmonic lattice potential, relevant to current experiments using optical lattices. We give corrections to the critical temperature arising from effective mass modifications of the low energy spectrum, finite size effects and excited band states. We compute the critical temperature using numerical methods and compare to our analytic result. We study condensation in an optical lattice over a wide parameter regime and demonstrate that the critical temperature can be increased or reduced relative to the purely harmonic case by adjusting the harmonic trap frequency. We show that a simple numerical procedure based on a piecewise analytic density of states provides an accurate prediction for the critical temperature.Comment: 10 pages, 5 figure

A first step toward higher order chain rules in abelian functor calculus

One of the fundamental tools of undergraduate calculus is the chain rule. The notion of higher order directional derivatives was developed by Huang, Marcantognini, and Young, along with a corresponding higher order chain rule. When Johnson and McCarthy established abelian functor calculus, they proved a chain rule for functors that is analogous to the directional derivative chain rule when $n = 1$. In joint work with Bauer, Johnson, and Riehl, we defined an analogue of the iterated directional derivative and provided an inductive proof of the analogue to the chain rule of Huang et al. This paper consists of the initial investigation of the chain rule found in Bauer et al., which involves a concrete computation of the case when $n=2$. We describe how to obtain the second higher order directional derivative chain rule for abelian functors. This proof is fundamentally different in spirit from the proof given in Bauer et al. as it relies only on properties of cross effects and the linearization of functors

Sigma_c Dbar and Lambda_c Dbar states in a chiral quark model

The S-wave Sigma_c Dbar and Lambda_c Dbar states with isospin I=1/2 and spin S=1/2 are dynamically investigated within the framework of a chiral constituent quark model by solving a resonating group method (RGM) equation. The results show that the interaction between Sigma_c and Dbar is attractive, which consequently results in a Sigma_c Dbar bound state with the binding energy of about 5-42 MeV, unlike the case of Lambda_c Dbar state, which has a repulsive interaction and thus is unbound. The channel coupling effect of Sigma_c Dbar and Lambda_c Dbar is found to be negligible due to the fact that the gap between the Sigma_c Dbar and Lambda_c Dbar thresholds is relatively large and the Sigma_c Dbar and Lambda_c Dbar transition interaction is weak.Comment: 7 pages,2 figures. arXiv admin note: text overlap with arXiv:nucl-th/0606056 by other author

Hertz-level Measurement of the 40Ca+ 4s 2S1/2-3d 2D5/2 Clock Transition Frequency With Respect to the SI Second through GPS

We report a frequency measurement of the clock transition of a single ^40Ca^+ ion trapped and laser cooled in a miniature ring Paul trap with 10^-15 level uncertainty. In the measurement, we used an optical frequency comb referenced to a Hydrogen maser, which was calibrated to the SI second through the Global Positioning System (GPS). Two rounds of measurements were taken in May and June 2011, respectively. The frequency was measured to be 411 042 129 776 393.0(1.6) Hz with a fractional uncertainty of 3.9{\times}10^-15 in a total averaging time of > 2{\times}10^6 s within 32 days

Adhesion-induced lateral phase separation of multi-component membranes: the effect of repellers and confinement

We present a theoretical study for adhesion-induced lateral phase separation for a membrane with short stickers, long stickers and repellers confined between two hard walls. The effects of confinement and repellers on lateral phase separation are investigated. We find that the critical potential depth of the stickers for lateral phase separation increases as the distance between the hard walls decreases. This suggests confinement-induced or force-induced mixing of stickers. We also find that stiff repellers tend to enhance, while soft repellers tend to suppress adhesion-induced lateral phase separation